Precalculus Examples

$\frac{\tan (a)}{\cot (a)}$

Step 1

Rewrite $\cot (a)$ in terms of sines and cosines.

$\frac{\tan (a)}{\frac{\cos (a)}{\sin (a)}}$

Step 2

Rewrite $\tan (a)$ in terms of sines and cosines.

$\frac{\frac{\sin (a)}{\cos (a)}}{\frac{\cos (a)}{\sin (a)}}$

Step 3

Multiply by the reciprocal of the fraction to divide by $\frac{\cos (a)}{\sin (a)}$ .

$\frac{\sin (a)}{\cos (a)} \cdot \frac{\sin (a)}{\cos (a)}$

Step 4

Simplify.

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Step 4.1

Convert from $\frac{\sin (a)}{\cos (a)}$ to $\tan (a)$ .

$\tan (a) \frac{\sin (a)}{\cos (a)}$

Step 4.2

Convert from $\frac{\sin (a)}{\cos (a)}$ to $\tan (a)$ .

$\tan (a) \tan (a)$

Step 4.3

Raise $\tan (a)$ to the power of $1$ .

$\tan^{1} (a) \tan (a)$

Step 4.4

Raise $\tan (a)$ to the power of $1$ .

$\tan^{1} (a) \tan^{1} (a)$

Step 4.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\tan (a)}^{1 + 1}$

Step 4.6

Add $1$ and $1$ .

$\tan^{2} (a)$